PCAT Quantitative Reasoning – Logarithms and Exponents
 by
 Apr 19, 2018
 PCAT Question of the Day
Log_{4}8^{3} is closest in value to which of the following?
A. 3.5
B. 4
C. 4.5
D. 5
Click for Explanation
C is correct. First, let’s expand 8^{3} and express this value in terms of 4:
log_{4}8^{3} = log_{4}(8 × 8 × 8) = log_{4}(4 × 2 × 4 × 2 × 4 × 2) = log_{4}(4^{3} × 2^{3}) = log_{4}(4^{4} × 2)
We know the relationship between logarithmic and exponential expressions to be log_{a}b = c and a^{c} = b, so let’s rewrite this expression as such:
4^{x} = 4^{4} × 2
Therefore, we know that our answer must be greater than x = 4 (4^{4} = 256) but less than x = 5 (4^{5} = 1024). Answer choice C is correct: 4^{4.5} = 8^{3} = 512.
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